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A278668
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Expansion of Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^3 in powers of x.
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2
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1, 3, 9, 22, 51, 107, 218, 420, 788, 1428, 2531, 4375, 7430, 12377, 20313, 32833, 52402, 82585, 128750, 198588, 303428, 459375, 689710, 1027243, 1518709, 2229375, 3251022, 4710777, 6785378, 9717677, 13841991, 19614182, 27656250, 38810312, 54216128, 75406438
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^3.
a(n) ~ exp(2*Pi*sqrt(7*n/15)) * 7^(3/4) / (20 * 3^(3/4) * 5^(1/4) * n^(5/4)). - Vaclav Kotesovec, Nov 10 2017
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EXAMPLE
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G.f.: 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 107*x^5 + 218*x^6 + ...
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Product[(1 - x^(5*k))/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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